Probing aqueous ions with non-local Auger relaxation

Non-local analogues of Auger decay are increasingly recognized as important relaxation processes in the condensed phase. Here, we explore non-local autoionization, specifically Intermolecular Coulombic Decay (ICD), of a series of aqueous-phase isoelectronic cations following 1s core-level ionization. In particular, we focus on Na+, Mg2+, and Al3+ ions. We unambiguously identify the ICD contribution to the K-edge Auger spectrum. The different strength of the ion–water interactions is manifested by varying intensities of the respective signals: the ICD signal intensity is greatest for the Al3+ case, weaker for Mg2+, and absent for weakly-solvent-bound Na+. With the assistance of ab initio calculations and molecular dynamics simulations, we provide a microscopic understanding of the non-local decay processes. We assign the ICD signals to decay processes ending in two-hole states, delocalized between the central ion and neighbouring water. Importantly, these processes are shown to be highly selective with respect to the promoted water solvent ionization channels. Furthermore, using a core-hole-clock analysis, the associated ICD timescales are estimated to be around 76 fs for Mg2+ and 34 fs for Al3+. Building on these results, we argue that Auger and ICD spectroscopy represents a unique tool for the exploration of intra- and inter-molecular structure in the liquid phase, simultaneously providing both structural and electronic information.

Curve fitting of ICD and photoelectron peaks of AlCl 3 and MgCl 2 spectra measured with hν 1572.9 eV and 1318.15 eV, respectively. The Voigt profiles that are used to fit the ICD structure correspond to different water valence band orbitals, 1b 1 (yellow), 3a 1 (green), 1b 2 (blue), and 2a 1 (purple) for both ICD 2p and ICD 2s .
Supplementary Fig. S3 Na, Mg and Al 1s core level photoelectron spectra from aqueous 1 M NaCl, 1 M MgCl 2 and 2 M AlCl 3 solutions. The Mg 1s spectrum is from a separate calibration experiment, see text for details. −1.75(20), and −2.1(4) eV being determined for the NaCl, MgCl 2 , and AlCl 3 -experiments, which is well in agreement with our experience from other calibration runs at the P04 beamline. The kinetic energy scale for the Na and Mg ICD spectra was then calibrated using the corrected photon energy together with binding energies taken from Ref. 2 Table S1.

and collected in
It has recently been shown that binding energies (or, more precisely, vertical ionization energies) in the liquid state can be measured on an absolute scale by referring to the cutoff formed by zero-kinetic energy electrons when a negative bias is applied to the liquid jet. 1,7 This approach, although correct, has not been used here; we instead pragmatically refer binding energies for the Na 1s, Mg 1s and Al 1s features for the solutions in question to the binding energy of the O 1s feature, setting it to its value of 538.1±0.1 eV found in neat liquid water. 1,3 By that, we are sensitive to the potential influence of a streaming potential on our Supplementary Tab. S1 Binding energies used in this work, in eV. Values for the 1s levels were determined in this work, and are based on an O 1s binding energy for neat liquid water of 538.1 eV. 1,3 In cases of the NaCl and AlCl 3 solutions this value was used as a proxy for the O 1s binding energy in the electrolyte solution. 4 We averaged over the two fine-structure levels of the 2p vacancy state. Original values from Ref. 2 were given without a stated accuracy; the error shown here is our estimate considering the methodology employed in this work. Values given for the valence states of water are calculations from this work for water molecules in the first solvation shell of the respective metal center, see Tab We estimate the potential error due to these shortcomings by considering the magnitude of the underlying effects: 1. Streaming potentials for highly conductive solutions were found to roughly vary between 0.1 and 0.3 eV. 8 2. The absolute change in binding energy of water valence and solvent peaks between neat water and 2 M NaI solution was found to not exceed 0.1 eV. 7 To account for these two factors, we increase the error of binding energies determined in the course of this work by 0.2 eV. The binding energy of the Na 1s state in 1 M aqueous NaCl solution was calibrated against the O 1s line of the same solution, measured back-to-back at equal photon energy and pass energy, giving 1076.7(4) eV independent of any photon energy and kinetic energy calibrations. A slightly higher value, but within the given error, is read from Fig. S3.
The binding energy of the Mg 1s state in 1 M aqueous MgCl 2 solution was determined in a separate experiment using the SOL 3 PES setup at the U49/2 PGM1 beamline of BESSY II at Helmholtz-Zentrum Berlin für Materialien und Energie. 9,10 Here, firstly the photon-energy scale was calibrated by measuring the O 1s feature of the solution with first and second diffraction order light from the monochromator. Then measuring neat water (with 50 mM NaCl added), the kinetic-energy scale of the analyzer was calibrated to a value of 538.1 eV for the O 1s peak. 1 A spectrum of the Mg 1s peak recorded using the calibrated photon energy and kinetic-energy scales then yielded a binding energy of 1309.9(4) eV, where the error contains estimates for the inaccuracy of the peak-position determination, the linearity of the analyzer energy scale, the error of literature binding energy, and contributions from the streaming potential and solute-induced binding-energy changes as outlined above. The photon energy was set to 1410.5(1) eV for this measurement.
For the measurements of the Al 3+ electrolyte, a different route had to be taken due to the photon-energy limitations of the U49/2 PGM1 beamline, resulting in it being impossible to measure the Al 1s photoemission feature in the BESSY II calibration experiments. Similarly to the Mg 2+ experiment, the photon energy was calibrated by measuring first and second diffraction order light from the monochromator. Then the kineticenergy scale of the analyzer was calibrated to a value of 538.1 eV for the O 1s peak. 1,3 Here, however, due to lack of time, no separate measurement of the O 1s peak could be carried out from neat liquid water. Instead we used the literature value for neat liquid water as a proxy for the O 1s peak of the 2 M AlCl 3 solution. A measurement of the Al KLL Auger peak (see the left hand panel of Fig. 2(a)), with the main feature being fitted by an exponentially modified Gaussian profile, then yielded a kinetic energy of 1380.9(4) eV; the error includes a 0.2 eV contribution representing potential changes of the O 1s binding energy in AlCl 3 solution versus water. We used this value for Al KLL to calibrate the kinetic-energy scale of our Al ICD experiment, and subsequently determined the photon-energy correction for that experiment given above. From the Al ICD set of measurements at PETRA, a scan over the Al 1s feature at a photon energy of 1750 eV yielded a binding energy of 1567.75 eV, with the same corrections applied. This same spectrum, calibrated against the O 1s feature of AlCl 3 solution recorded back-to-back, yields a binding energy of 1567.63 eV, when again 538.1 eV is used as the O 1s binding energy in the solution. We summarize these two measurements as 1567.7(4) eV.
Finally, in a third experiment we tested for the consistency of the two binding-energy values determined as described above, by measuring Mg 1s of 1 M MgCl 2 solution and Al 1s of 2 M AlCl 3 solution with equal photon energy of 1760 eV (nominal value of the beamline, no correction attempted). This set of spectra yielded a binding-energy difference of the two features of 258.7 eV, while the data given above differ by 257.8 eV. This disagreement is outside of the error bars given above for the 1s measurements, albeit not by much. We point out that in this experiment Mg 1s was measured at 1760 eV photon energy, while our other experiment was at 1410.5 eV. (For Al 1s practically equal photon energies were used.) Although the binding energy should be independent of photon energy, effects like post-collision interaction in principle could contribute to the discrepancy of the two measurements we have observed. At this moment this point is speculative, however. In order to reflect our uncertainty about the true 1s binding energies, we have increased the error bars of the input values to the calculation of the expected two-hole final state energies ( Fig. 7 and Tables S2 and S3) to ±1 eV. This contribution to the systematic error manifests itself as an overall shift of all experimental Mg 2+ or Al 2+ energies, which is not essential for the conclusions in this paper.
For the water valence single vacancy states we found it most adequate to use the binding energies calculated in this work specifically for a water molecule directly coordinated to the respective metal center, since it it these water molecules that primarily take place in ICD of a metal vacancy. As discussed in the main text and summarized again in Tab. S5 of the Supplementary Information, these may differ notably from values found for neat liquid water.
Supplementary Tab. S2 The experimental ICD electron kinetic energies and two-hole energies. E k (est.) is the energy estimated from the binding energies of the orbitals involved in the decay. E k (meas.) is the experimentally measured kinetic energy. The Coulomb penalty, E Cp is the difference between E k (est.) and E k (meas.). The two-hole energy was obtained as E 2h = E 1s − E k (meas.), and is shown in Fig. 7. E 1s (Mg 2+ ) = 1309.9 eV, E 1s (Al 3+ ) = 1567.7 eV. The associated data are collected for Al 3+ and Mg 2+ , measured with the lower of two hν-values used in our experiments, 1569.8 eV and 1315.25 eV, respectively. The final-state designation denotes first the vacancy in the metal center, second the vacancy in the surrounding water solvation shell. All energies are given in eV.

Final
Al The energy estimated for the ICD peaks, their measured energy, and the difference of these two numbers ('Coulomb penalty'), are given in Table S2 for the measurements shown in Fig. 4 of the main manuscript (lower photon energy), and in Table S3 for the measurements at higher photon shown in Fig. S2 The ICD features are independent of the photon energy, therefore, the kinetic energies of these broad peaks are similar in both measurements. The values for the Coulomb penalty are also in the same range. The columns 'E k (est.)' and 'E 2h ' are subject to a systematic error in the measurement of the 1s binding energy, which may lead to a common shift of all Mg or Al data points by ±1 eV, see above. Errors for the line positions retrieved by the peak fitting are estimated as ±0.5 eV for states involving a 3a 1 or 1b 2 vacancy, ±0.8 eV for 2p −1 1b −1 1 states and ±1 eV for 2s −1 1b −1 1 states and those involving a 2a 1 vacancy. Molecular dynamics. In order to generate a set of structures, we performed classical molecular simulations of NaCl, MgCl 2 , and AlCl 3 solutions. These classical non-polarizable force fields allowed us to perform long molecular simulations for relatively large-scale systems. In this way, we could account for long-range polarizability in subsequent QM/MMPol calculations. The parameters for classical simulations were taken from the literature to best represent the radial distribution functions for the cation-water oxygen. We regard this parameter as crucial for subsequent calculations of the ICD states. Note, that for the magnesium cation, we used the Electronic Continuum Correction (ECC), 11,12 which employs scaled charges and a slightly modified van der Waals radius of the ions in order to best reproduce neutron scattering data specifically for the Mg-O distance in solution. Details of the classical simulations together with the Lennard-Jones parameters used in the simulations are provided in Table S4. The force field for MgCl 2 was taken from Ref. 13 and for NaCl from Ref. 14. The aluminium parameters were taken from Ref. 15. Water was in all cases simulated by the SPC/E model. 16 The classical simulations were performed for 1 M solutions for NaCl and MgCl 2 and for 2 M solution for AlCl 3 to match the experiment.
The simulation box for both NaCl and MgCl 2 contained 160 molecules of salt and an appropriate number of water molecules to match the respective density (8753 water molecules for NaCl and 8810 for MgCl 2 ). For AlCl 3 , the simulation box contained 267 aluminium cations, 801 chloride anions, and 8472 water molecules. The total length of each simulation was 200 ns, the time step for the propagation was set to 2 fs, and 3D periodic boundary conditions were employed. The simulation temperature was set to 300 K and was controlled by a velocity-rescale thermostat with time coupling set to 0.5 ps (0.1 ps for AlCl 3 ). The pressure of the system was set to 1 bar which was controlled by the Parrinello-Rahman barostat 17 with a coupling constant of 1 ps (2 ps for AlCl 3 ). The LINCS 18 constrain algorithm of fourth order was applied to all bonds. The van der Waals interactions were truncated at 1.5 nm (1.2 nm for AlCl 3 ); the long-range electrostatic interactions were calculated by the particle mesh Ewald method.
Population analysis. The preference of ICD electron emission from specific molecular orbitals can also  be conveniently demonstrated for the [Al(H 2 O) 5 Cl] 2+ complex. In this complex, the chloride p orbitals can be either perpendicular (3p x and 3p y ) or parallel (3p z ) to the connecting line between chloride and the central cation. The orbital overlap between the chloride anion and the central ion is very different in the two cases. The Löwdin reduced orbital population per molecular orbital shows that the p x and p y molecular orbitals are localized only to less than 2% on the central cation while the contribution amounts to 13% for p z . Since the ICD signal intensity should be proportional to the overlap between the orbitals of the ionized cation and of the neighbouring molecule, we can suppose that the signal arising from the 3p z orbital of chloride would be quite strong. On the same basis, we can suppose that the 3s contribution would be much smaller.
Supplementary Fig. S5 Selected molecular orbitals for the [Al(H 2 O) 5 Cl] 2+ complex. The Löwdin reduced orbital population per molecular orbital was performed at the BH&HLYP 6-31+g* level in the polarizable continuum, respective molecular orbitals are depicted with an isovalue of 0.05 e.
Electronic structure of water in the first solvation shell. For conciseness, we summarize here the results of our electronic structure calculations for water in the first solvation shell of a metal cation, see Fig. 6 in the main text. Experimental binding energies for neat liquid water are shown for comparison, and were derived by using the recent absolute measurement of water's vertical ionization energy 1 for the 1b 1 level, and the 1b 1 -3a 1 , 1b 1 -1b 2 and 1b 1 -2a 1 energy gaps from Ref. 19

Orbitals
Na Calculated binding energies and ICD energies in the gas phase. In Supplementary Tables S8 and S9 we give the orbital energies and two-hole state energies for a minimal model consisting of a metal-water dimer, calculated without taking the effects of a polarizable medium (the surrounding water environment) into account. Supplementary Tab. S8 Two-hole energies like in Supplementary Table S6, for a minimal model containing one cation and one water molecule in the gas phase. The values of E b,vi are provided in Table S9. *Due to convergence issues, less than 20 calculations were performed. The SCF convergence for ICD states involving the 3a 1 water orbital was very poor, therefore the data are missing.  Supplementary Table S7, for a minimal model containing one cation and one water molecule in the gas phase.